SEGURO PARA PENSIONES DE INVALIDEZ Y SOBREVIVENCIA CAUSADAS DURANTE LA VIDA ACTIVA DE LOS AFILIADOS.

In this section, we consider the model of energy consumption developed in [164]. This model has been used in several contexts to evaluate the energy consumption of systems SISO and MIMO cooperative in sensor networks [165], [166]. The max−dmin protocol employs

138 Chapter 5 : Cooperative Closed-loop MIMO Systems

Figure 5.18: Performance comparison between coded and uncoded MIMO for max−dmin

Precoding with FCSI under RapSor channel.

cooperative MIMO with the distributed nodes serving as multiple antennas. Hence, we are involved in the total energy consumption E_coop of the nodes for full communication. According to the protocol description, the total energy of the cooperating nodes can now be expressed as

E_coop= E_loc+ E_init+ E_fbk+ EM IM O (5.34)

where E_loc is the local transmission energy, i.e., the SISO communication between the nodes, E_init is the initialization phase, E_fbk is the feedback control channel energy, and

EM IM O is the energy of the data packet for MIMO transmission.

The average energy consumption of a radio frequency (RF) system can broadly be separated into PAmp and Pcctwhich are the power consumption of power amplifiers and other circuits

blocks, respectively. The model of typical RF blocks [164] representing the emitter is depicted in Fig. 5.20, while the receiver can be seen in Fig. 5.21. The PAmp is expressed

as PAmp = ς εPout = ς ε Eb N₀ (4π)2dL_0L mDr AgtAgrλ2 Rb (5.35)

ς is the peak-to-average ratio (PAR), ε corresponds to the power amplifier efficiency, Eb

N0 is

the ratio energy per bit to the noise, Agt, and Agrare the emitter and the receiver antenna

Figure 5.19: BER performance for max−dmin MIMO precoding with FCSI under RapSor

channel with node selection.

Figure 5.20: Transmitter circuit block.

the hardware process and other noises, λ is the wavelength, Dr is the power density at

the receiver, d is the long-haul distance, L₀ is the path-loss component, and Rb is the bit

rate. The total power dissipated in circuit, Pcct for nt transmitters and nr receivers can be

approximately expressed as

Pcct= (PDAC + Pf ilt+ Pmix+ Psynth) + (Pf ilr+ PLN A+ Pmix+ PIF A+ Psynth+ PADC)

= ntPcT x+ nrPcRx

140 Chapter 5 : Cooperative Closed-loop MIMO Systems

Figure 5.21: Receiver circuit block.

where PDAC and PADC are consumed energy for the digital-to-analog converter (DAC) and

the analog-to-digital converter (ADC), respectively. Pf ilt is the power consumed for the

active filters at the transmitter, whereas Pmix and Pf ilr are the energy consumed for the

mixer and the active filters at the receiver, respectively. PLN A, Psynth, and PIF A are power

consumption for the Low-Noise Amplifier (LNA), the frequency synthesizer, and the In- termediate Frequency Amplifier, respectively. Parameter P_cT x represents power dissipated in the circuit for a single node during data transmission, and PRx

c for the reception. Total

energy consumed per bit, Ebit for a fixed-rate system is evaluated in equation (5.37)

Ebit =

PAmp+ Pcct

Rb

(5.37)

Assuming a packet size of D symbols is to be transmitted, and training symbols size of pnt

is inserted (each node transmits p symbols), the effective bit rate Ref f_b is

Ref f_b =  D− pnt D  Rb (5.38)

Note that replacing Rb in equation (5.35) by Ref fb , we obtained the energy consumption

model which accounts for the additional energy due to the p training symbols.

For the max−dmin MIMO precoding transmission, the bit rate Rb can thus be calculated

as follows

Rb = RmB (5.39)

where R is the MIMO transmission rate, expressed as a ratio of the number of symbols transmitted, NS, over the number of periods, NP, (i.e., R = NS/NP). m = log₂(M ), where

M is the constellation size, and B is the modulation bandwidth. The parameter, Eloc is

the total local transmission energy expended within a cluster k that consists of nc nodes,

separated by an average distance of dc. Each source node can transmit to nr = (nc− 1)

receivers. Thus, Eloc is expressed as

Eloc= Npkt  PAmp+ Pcct R_bef f  withPcct= PcT xk+ (nc− 1)PcRxk (5.40)

Table 5.1: Nodes and PAR parameters for energy computation

Parameters Values

Gains Gr and Gt 2.5 dBi

Frequency carrier fc 2.5 GHz

Bandwidth 20 MHz Power Amp. Efficiency ε 0.35

BER 10e−4

where Npkt= ncL is the total number of bits in all sent packets, and for the random nodes

cooperative transmission scenario, nc = nt. In (5.41), the training phase energy, Einit is

given, where NT s is the number of training bits

Einit= NT s  PAmp+ Pcct ROST BC b  withPcct= (nc)PcT xk (5.41)

Only Alamouti’s code yields a rate, R = 1 for complex modulations. The OSTBC solution for any value of nt but with R = 1/2 is presented in [167]. Solutions for nt = 3 and 4,

but with R = 3/4 are similarly performed. To implement our training phase for 10 (nc)

cluster nodes, we consider 4× 4 OSTBC transmissions. Then, we average rate to obtain

R_bOST BC = 2/3, and the Eb/N0 at the target BER. On the feedback channel, the energy

Ef bk consumed is Ef bk =  Nf bk ntPcctRxk Rb  (5.42) where nt sensor nodes act as receivers in this case, Nf bk is the number of bits sent on the

feedback channel. The values of 3, 5, and 7 bits are considered for Nf bk when 2, 3, and 4

nodes are selected, respectively. Note that max−dmin based selection requireslog₂L bits

which have been included inNf bk, where. denotes the nearest higher integer. The energy

needed for the transmission of the data packets by MIMO technique using the max−dmin

precoder is EM IM O = Npkt  PAmp+ Pcct Ref f_b −prec  withPcct= (nt)PcT xk (5.43)

R_b(.) is the efficiency of the MIMO technique used in transmitting the symbols over b sub- channels. Hence Ref f_b −prec = 2.